We present and discuss new spectroscopic observations of the unusual galaxy J2310-43. The observations cover a wide wavelength range, from 3700 Angstrom to 9800 Angstrom allowing the study of both the regions where H alpha and the Ca II ''contrast'' are expected. No evidence for H alpha in emission is found and we thus confirm the absence of emission lines in the spectrum of J2310-43, ruling out the possibility that it may host a Seyfert nucleus. The Ca II break is clearly defected and the value of the contrast. (38%+/-4%) is intermediate between that of a typical elliptical galaxy (approximate to 50%) and that of a BL Lac object (less than or equal to 25%). This result imposes limits on the intensity of a possible non-stellar continuum and, in the light of the radio and X-ray loudness of the source, draws further attention to the problem of the recognition of a BL Lac object. Objects like J2310-43 may be more common than previously recognized, and begin to emerge in surveys of radio-emitting X-ray sources. (C) 1997 The American Astronomical Society. [S0004-6256(97)03712-6].